fables
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fables [2023/02/12 13:07] – kalinin0 | fables [2023/02/28 16:53] – kalinin0 | ||
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====== Séminaire " | ====== Séminaire " | ||
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+ | Monday, March 6, 2023 | ||
+ | room 6-13 | ||
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+ | **15h00 — Ali Ulaş Özgür Kişisel** | ||
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+ | **Expected measures of amoebas of random plane curves** | ||
+ | |||
+ | There are several natural measures that one can place on the amoeba of an algebraic curve in the complex projective plane. Passare and Rullgård prove that the total mass of the Lebesgue measure on the amoeba of a degree $d$ curve is bounded above by $π^{2} d^{2} / 2$, by comparing it to another Monge-Ampère type measure, which is dual to the usual measure on the Newton polytope of the defining polynomial via the Legendre transform. Mikhalkin generalizes this upper bound to half-dimensional complete intersections in higher dimensions, by considering another measure supported on their amoebas; their multivolume. The goal of this talk will be to discuss these measures in the setting of random plane curves. In particular, I’ll first present our results with Bayraktar, showing that the expected multiarea of the amoeba of a random Kostlan degree $d$ curve is equal to $π^2 d$. For Lebesgue measure, it turns out that the expected asymptotics are much lower: I’ll describe our results with Welschinger, | ||
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Ligne 6: | Ligne 17: | ||
room 6-13 | room 6-13 | ||
- | **15h00 Evgeni Abakoumov (Paris/ | + | **15h00 |
**Chui' | **Chui' | ||
- | Abstract: | + | C. K. Chui conjectured in 1971 that the average gravitaional field strength in the unit disk due to unit point masses on its boundary was the smallest when these point masses were equidistributed on the circle. We will present an elementary solution to some weighted versions of this problem, and discuss related questions concerning approximation of holomorphic functions by simple partial fractions. This is joint work with A. Borichev and K. Fedorovskiy. |
- | ** 16h00 Ferit Ozturk (Istanbul/ | + | **16h00 |
**Every real 3-manifold admits a real contact structure** | **Every real 3-manifold admits a real contact structure** | ||
- | Abstract: | + | We survey our results regarding real contact 3-manifolds and present our result in the title. |
A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, called a real structure. | A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, called a real structure. | ||
A real contact 3-manifold is a real 3-manifold with a contact distribution that is antisymmetric with respect to the real structure. | A real contact 3-manifold is a real 3-manifold with a contact distribution that is antisymmetric with respect to the real structure. |
fables.txt · Dernière modification : 2023/12/05 11:54 de slavitya_gmail.com